How to detect patterns in salary distribution if we are suspecting malicious distribution based on employee's region?
A simple initial approach would be to separate it by position and check for each:

Use linear regression: $\hat{salary} = \sum_i \alpha_i * \hat{region}_i + \sum_k \beta_k * \mathbf{1}[\hat{gender}=k]$ and now you have an intuitive measure by looking at $\alpha$'s and $\beta$'s. 

2 issues that may arise with this method:


This assumes though that a linear model is a good fit, which it very well might not be   
The amount of data points may be small and this will give you point estimates without any sense of confidence.   


2 possible respective solutions:  


Use a stronger model with less intuitive parameters (like a neural network) and then use common visualization techniques to determine weight of each input (this could be as simple as changing them and looking at the outcome or something more complex that utilizes the gradient), but even more complex models can still suffer from the second problem, which is why id reccommend option 2
Use a Bayesian model, you can make something hierarchical something as simple as doing the above linear regression with a non informative prior and eventually you'd be able to build confidence intervals and get a better sense of the associations (note if youre looking for what to write this in, I recommend JAGS for its ease of use)